This question came up in my class, and I'm meant to answer it thematically (although I don't necessarily need the answer in this thread to be thematically). I sought of generally put it down to Greece's natural geography/weather vs. Persia's, hoplite warfare and the unity and leadership of the Greeks. Any help would be appreciated.
The Cambridge History of Warfare is a pretty good source on this, and the short answer is that greek war style was so different that they had no counter to the persian style for a while. Greek war was almost like a team match, while persians fought more pragmatically.